Chipman, Hugh AGeorge, Edward IMcCulloch, Robert E2023-05-232023-05-232002-07-012016-07-11https://repository.upenn.edu/handle/20.500.14332/47936When simple parametric models such as linear regression fail to adequately approximate a relationship across an entire set of data, an alternative may be to consider a partition of the data, and then use a separate simple model within each subset of the partition. Such an alternative is provided by a treed model which uses a binary tree to identify such a partition. However, treed models go further than conventional trees (e.g. CART, C4.5) by fitting models rather than a simple mean or proportion within each subset. In this paper, we propose a Bayesian approach for finding and fitting parametric treed models, in particular focusing on Bayesian treed regression. The potential of this approach is illustrated by a cross-validation comparison of predictive performance with neural nets, MARS, and conventional trees on simulated and real data sets.The final publication is available at Springer via http://dx.doi.org/10.1023/A:1013916107446.binary treesMarkov chain Monte Carlomodel selectionstochastic searchStatistics and ProbabilityArticle